BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND OPTIMAL CONTROL OF MARKED POINT PROCESSES

被引:24
|
作者
Confortola, Fulvia [1 ]
Fuhrman, Marco [1 ]
机构
[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy
关键词
backward stochastic differential equations; optimal control problems; marked point processes; JUMPS;
D O I
10.1137/120902835
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution on the data. We next address optimal control problems for point processes of general non-Markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function. Finally we introduce a Hamilton-Jacobi-Bellman equation, also stochastic and of backward type, for this class of control problems: when the state space is finite or countable we show that it admits a unique solution which identifies the (random) value function and can be represented by means of the BSDEs introduced above.
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页码:3592 / 3623
页数:32
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